Let a and b be the roots of x^2 - 34x + 34 = 0. What is (a + 1)(b + 1)?
The roots of x^2 - 34x + 34 = 0 are 17 + sqrt 255 and 17 - sqrt 255
then (a + 1)(b + 1) = (18 + sqrt255)(18-sqrt255) Can you calculate the answer from here?
ab = 34, a+b=34,
so,
(a + 1)(b + 1) = ab + a + b + 1 = 34+ 34 +1 = 69.
Great! I got the same answer, but I like your method better !